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dc.contributor.authorAlsing, Paul M.
dc.contributor.authorMiller, Warner A.
dc.contributor.authorCorne, Matthew
dc.contributor.authorGu, David
dc.contributor.authorLloyd, Seth
dc.contributor.authorRay, Shannon
dc.contributor.authorYau, Shing-Tung
dc.date.accessioned2018-12-21T19:28:58Z
dc.date.available2018-12-21T19:28:58Z
dc.date.issued2015-01
dc.identifier.issn2328-8876
dc.identifier.issn2328-8884
dc.identifier.urihttp://hdl.handle.net/1721.1/119822
dc.description.abstractWe examine a Type-1 neck pinch singularity in simplicial Ricci flow (SRF) for an axisymmetric piecewise flat 3-dimensional geometry with topology S³. SRF was recently introduced as an unstructured mesh formulation of Hamilton’s Ricci flow (RF). It describes the RF of a piecewise-flat simplicial geometry. In this paper, we apply the SRF equations to a representative double-lobed axisymmetric piecewise flat geometry with mirror symmetry at the neck similar to the geometry studied by Angenent and Knopf (A-K). We choose a specific radial profile and compare the SRF equations with the corresponding finite-difference solution of the continuum A-K RF equations. The piecewise-flat 3-geometries considered here are built of isosceles-triangle-based frustum blocks. The axial symmetry of this model allows us to use frustum blocks instead of tetrahedra. The S² cross-sectional geometries in our model are regular icosahedra. We demonstrate that, under a suitably-pinched initial geometry, the SRF equations for this relatively low-resolution discrete geometry yield the canonical Type-1 neck pinch singularity found in the corresponding continuum solution. We adaptively remesh during the evolution to keep the circumcentric dual lattice wellcentered. Without such remeshing, we cannot evolve the discrete geometry to neck pinch. We conclude with a discussion of future generalizations and tests of this SRF model.en_US
dc.publisherInternational Press of Bostonen_US
dc.relation.isversionofhttp://dx.doi.org/10.4310/GIC.2014.V1.N3.A1en_US
dc.rightsCreative Commons Attribution-Noncommercial-Share Alikeen_US
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/4.0/en_US
dc.sourcearXiven_US
dc.titleSimplicial Ricci flow: an example of a neck pinch singularity in 3Den_US
dc.typeArticleen_US
dc.identifier.citationAlsing, Paul M. et al. “Simplicial Ricci Flow: An Example of a Neck Pinch Singularity in 3D.” Geometry, Imaging and Computing 1, 3 (2014): 303–331 © 2014 International Press of Bostonen_US
dc.contributor.departmentMassachusetts Institute of Technology. Department of Mechanical Engineeringen_US
dc.contributor.mitauthorLloyd, Seth
dc.relation.journalGeometry, Imaging and Computingen_US
dc.eprint.versionOriginal manuscripten_US
dc.type.urihttp://purl.org/eprint/type/JournalArticleen_US
eprint.statushttp://purl.org/eprint/status/NonPeerRevieweden_US
dc.date.updated2018-12-13T14:51:38Z
dspace.orderedauthorsAlsing, Paul M.; Miller, Warner A.; Corne, Matthew; Gu, David; Lloyd, Seth; Ray, Shannon; Yau, Shing-Tungen_US
dspace.embargo.termsNen_US
mit.licenseOPEN_ACCESS_POLICYen_US


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